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diyfp.h
1 // Tencent is pleased to support the open source community by making RapidJSON available.
2 //
3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
4 //
5 // Licensed under the MIT License (the "License"); you may not use this file except
6 // in compliance with the License. You may obtain a copy of the License at
7 //
8 // http://opensource.org/licenses/MIT
9 //
10 // Unless required by applicable law or agreed to in writing, software distributed
11 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
12 // CONDITIONS OF ANY KIND, either express or implied. See the License for the
13 // specific language governing permissions and limitations under the License.
14 
15 // This is a C++ header-only implementation of Grisu2 algorithm from the publication:
16 // Loitsch, Florian. "Printing floating-point numbers quickly and accurately with
17 // integers." ACM Sigplan Notices 45.6 (2010): 233-243.
18 
19 #ifndef RAPIDJSON_DIYFP_H_
20 #define RAPIDJSON_DIYFP_H_
21 
22 #include "../rapidjson.h"
23 
24 #if defined(_MSC_VER) && defined(_M_AMD64)
25 #include <intrin.h>
26 #pragma intrinsic(_BitScanReverse64)
27 #pragma intrinsic(_umul128)
28 #endif
29 
30 RAPIDJSON_NAMESPACE_BEGIN
31 namespace internal {
32 
33 #ifdef __GNUC__
34 RAPIDJSON_DIAG_PUSH
35 RAPIDJSON_DIAG_OFF(effc++)
36 #endif
37 
38 #ifdef __clang__
39 RAPIDJSON_DIAG_PUSH
40 RAPIDJSON_DIAG_OFF(padded)
41 #endif
42 
43 struct DiyFp {
44  DiyFp() : f(), e() {}
45 
46  DiyFp(uint64_t fp, int exp) : f(fp), e(exp) {}
47 
48  explicit DiyFp(double d) {
49  union {
50  double d;
51  uint64_t u64;
52  } u = { d };
53 
54  int biased_e = static_cast<int>((u.u64 & kDpExponentMask) >> kDpSignificandSize);
55  uint64_t significand = (u.u64 & kDpSignificandMask);
56  if (biased_e != 0) {
57  f = significand + kDpHiddenBit;
58  e = biased_e - kDpExponentBias;
59  }
60  else {
61  f = significand;
62  e = kDpMinExponent + 1;
63  }
64  }
65 
66  DiyFp operator-(const DiyFp& rhs) const {
67  return DiyFp(f - rhs.f, e);
68  }
69 
70  DiyFp operator*(const DiyFp& rhs) const {
71 #if defined(_MSC_VER) && defined(_M_AMD64)
72  uint64_t h;
73  uint64_t l = _umul128(f, rhs.f, &h);
74  if (l & (uint64_t(1) << 63)) // rounding
75  h++;
76  return DiyFp(h, e + rhs.e + 64);
77 #elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
78  __extension__ typedef unsigned __int128 uint128;
79  uint128 p = static_cast<uint128>(f) * static_cast<uint128>(rhs.f);
80  uint64_t h = static_cast<uint64_t>(p >> 64);
81  uint64_t l = static_cast<uint64_t>(p);
82  if (l & (uint64_t(1) << 63)) // rounding
83  h++;
84  return DiyFp(h, e + rhs.e + 64);
85 #else
86  const uint64_t M32 = 0xFFFFFFFF;
87  const uint64_t a = f >> 32;
88  const uint64_t b = f & M32;
89  const uint64_t c = rhs.f >> 32;
90  const uint64_t d = rhs.f & M32;
91  const uint64_t ac = a * c;
92  const uint64_t bc = b * c;
93  const uint64_t ad = a * d;
94  const uint64_t bd = b * d;
95  uint64_t tmp = (bd >> 32) + (ad & M32) + (bc & M32);
96  tmp += 1U << 31; /// mult_round
97  return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
98 #endif
99  }
100 
101  DiyFp Normalize() const {
102 #if defined(_MSC_VER) && defined(_M_AMD64)
103  unsigned long index;
104  _BitScanReverse64(&index, f);
105  return DiyFp(f << (63 - index), e - (63 - index));
106 #elif defined(__GNUC__) && __GNUC__ >= 4
107  int s = __builtin_clzll(f);
108  return DiyFp(f << s, e - s);
109 #else
110  DiyFp res = *this;
111  while (!(res.f & (static_cast<uint64_t>(1) << 63))) {
112  res.f <<= 1;
113  res.e--;
114  }
115  return res;
116 #endif
117  }
118 
119  DiyFp NormalizeBoundary() const {
120  DiyFp res = *this;
121  while (!(res.f & (kDpHiddenBit << 1))) {
122  res.f <<= 1;
123  res.e--;
124  }
125  res.f <<= (kDiySignificandSize - kDpSignificandSize - 2);
126  res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2);
127  return res;
128  }
129 
130  void NormalizedBoundaries(DiyFp* minus, DiyFp* plus) const {
131  DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary();
132  DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2) : DiyFp((f << 1) - 1, e - 1);
133  mi.f <<= mi.e - pl.e;
134  mi.e = pl.e;
135  *plus = pl;
136  *minus = mi;
137  }
138 
139  double ToDouble() const {
140  union {
141  double d;
142  uint64_t u64;
143  }u;
144  const uint64_t be = (e == kDpDenormalExponent && (f & kDpHiddenBit) == 0) ? 0 :
145  static_cast<uint64_t>(e + kDpExponentBias);
146  u.u64 = (f & kDpSignificandMask) | (be << kDpSignificandSize);
147  return u.d;
148  }
149 
150  static const int kDiySignificandSize = 64;
151  static const int kDpSignificandSize = 52;
152  static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
153  static const int kDpMaxExponent = 0x7FF - kDpExponentBias;
154  static const int kDpMinExponent = -kDpExponentBias;
155  static const int kDpDenormalExponent = -kDpExponentBias + 1;
156  static const uint64_t kDpExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
157  static const uint64_t kDpSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
158  static const uint64_t kDpHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);
159 
160  uint64_t f;
161  int e;
162 };
163 
164 inline DiyFp GetCachedPowerByIndex(size_t index) {
165  // 10^-348, 10^-340, ..., 10^340
166  static const uint64_t kCachedPowers_F[] = {
167  RAPIDJSON_UINT64_C2(0xfa8fd5a0, 0x081c0288), RAPIDJSON_UINT64_C2(0xbaaee17f, 0xa23ebf76),
168  RAPIDJSON_UINT64_C2(0x8b16fb20, 0x3055ac76), RAPIDJSON_UINT64_C2(0xcf42894a, 0x5dce35ea),
169  RAPIDJSON_UINT64_C2(0x9a6bb0aa, 0x55653b2d), RAPIDJSON_UINT64_C2(0xe61acf03, 0x3d1a45df),
170  RAPIDJSON_UINT64_C2(0xab70fe17, 0xc79ac6ca), RAPIDJSON_UINT64_C2(0xff77b1fc, 0xbebcdc4f),
171  RAPIDJSON_UINT64_C2(0xbe5691ef, 0x416bd60c), RAPIDJSON_UINT64_C2(0x8dd01fad, 0x907ffc3c),
172  RAPIDJSON_UINT64_C2(0xd3515c28, 0x31559a83), RAPIDJSON_UINT64_C2(0x9d71ac8f, 0xada6c9b5),
173  RAPIDJSON_UINT64_C2(0xea9c2277, 0x23ee8bcb), RAPIDJSON_UINT64_C2(0xaecc4991, 0x4078536d),
174  RAPIDJSON_UINT64_C2(0x823c1279, 0x5db6ce57), RAPIDJSON_UINT64_C2(0xc2109436, 0x4dfb5637),
175  RAPIDJSON_UINT64_C2(0x9096ea6f, 0x3848984f), RAPIDJSON_UINT64_C2(0xd77485cb, 0x25823ac7),
176  RAPIDJSON_UINT64_C2(0xa086cfcd, 0x97bf97f4), RAPIDJSON_UINT64_C2(0xef340a98, 0x172aace5),
177  RAPIDJSON_UINT64_C2(0xb23867fb, 0x2a35b28e), RAPIDJSON_UINT64_C2(0x84c8d4df, 0xd2c63f3b),
178  RAPIDJSON_UINT64_C2(0xc5dd4427, 0x1ad3cdba), RAPIDJSON_UINT64_C2(0x936b9fce, 0xbb25c996),
179  RAPIDJSON_UINT64_C2(0xdbac6c24, 0x7d62a584), RAPIDJSON_UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
180  RAPIDJSON_UINT64_C2(0xf3e2f893, 0xdec3f126), RAPIDJSON_UINT64_C2(0xb5b5ada8, 0xaaff80b8),
181  RAPIDJSON_UINT64_C2(0x87625f05, 0x6c7c4a8b), RAPIDJSON_UINT64_C2(0xc9bcff60, 0x34c13053),
182  RAPIDJSON_UINT64_C2(0x964e858c, 0x91ba2655), RAPIDJSON_UINT64_C2(0xdff97724, 0x70297ebd),
183  RAPIDJSON_UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), RAPIDJSON_UINT64_C2(0xf8a95fcf, 0x88747d94),
184  RAPIDJSON_UINT64_C2(0xb9447093, 0x8fa89bcf), RAPIDJSON_UINT64_C2(0x8a08f0f8, 0xbf0f156b),
185  RAPIDJSON_UINT64_C2(0xcdb02555, 0x653131b6), RAPIDJSON_UINT64_C2(0x993fe2c6, 0xd07b7fac),
186  RAPIDJSON_UINT64_C2(0xe45c10c4, 0x2a2b3b06), RAPIDJSON_UINT64_C2(0xaa242499, 0x697392d3),
187  RAPIDJSON_UINT64_C2(0xfd87b5f2, 0x8300ca0e), RAPIDJSON_UINT64_C2(0xbce50864, 0x92111aeb),
188  RAPIDJSON_UINT64_C2(0x8cbccc09, 0x6f5088cc), RAPIDJSON_UINT64_C2(0xd1b71758, 0xe219652c),
189  RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), RAPIDJSON_UINT64_C2(0xe8d4a510, 0x00000000),
190  RAPIDJSON_UINT64_C2(0xad78ebc5, 0xac620000), RAPIDJSON_UINT64_C2(0x813f3978, 0xf8940984),
191  RAPIDJSON_UINT64_C2(0xc097ce7b, 0xc90715b3), RAPIDJSON_UINT64_C2(0x8f7e32ce, 0x7bea5c70),
192  RAPIDJSON_UINT64_C2(0xd5d238a4, 0xabe98068), RAPIDJSON_UINT64_C2(0x9f4f2726, 0x179a2245),
193  RAPIDJSON_UINT64_C2(0xed63a231, 0xd4c4fb27), RAPIDJSON_UINT64_C2(0xb0de6538, 0x8cc8ada8),
194  RAPIDJSON_UINT64_C2(0x83c7088e, 0x1aab65db), RAPIDJSON_UINT64_C2(0xc45d1df9, 0x42711d9a),
195  RAPIDJSON_UINT64_C2(0x924d692c, 0xa61be758), RAPIDJSON_UINT64_C2(0xda01ee64, 0x1a708dea),
196  RAPIDJSON_UINT64_C2(0xa26da399, 0x9aef774a), RAPIDJSON_UINT64_C2(0xf209787b, 0xb47d6b85),
197  RAPIDJSON_UINT64_C2(0xb454e4a1, 0x79dd1877), RAPIDJSON_UINT64_C2(0x865b8692, 0x5b9bc5c2),
198  RAPIDJSON_UINT64_C2(0xc83553c5, 0xc8965d3d), RAPIDJSON_UINT64_C2(0x952ab45c, 0xfa97a0b3),
199  RAPIDJSON_UINT64_C2(0xde469fbd, 0x99a05fe3), RAPIDJSON_UINT64_C2(0xa59bc234, 0xdb398c25),
200  RAPIDJSON_UINT64_C2(0xf6c69a72, 0xa3989f5c), RAPIDJSON_UINT64_C2(0xb7dcbf53, 0x54e9bece),
201  RAPIDJSON_UINT64_C2(0x88fcf317, 0xf22241e2), RAPIDJSON_UINT64_C2(0xcc20ce9b, 0xd35c78a5),
202  RAPIDJSON_UINT64_C2(0x98165af3, 0x7b2153df), RAPIDJSON_UINT64_C2(0xe2a0b5dc, 0x971f303a),
203  RAPIDJSON_UINT64_C2(0xa8d9d153, 0x5ce3b396), RAPIDJSON_UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
204  RAPIDJSON_UINT64_C2(0xbb764c4c, 0xa7a44410), RAPIDJSON_UINT64_C2(0x8bab8eef, 0xb6409c1a),
205  RAPIDJSON_UINT64_C2(0xd01fef10, 0xa657842c), RAPIDJSON_UINT64_C2(0x9b10a4e5, 0xe9913129),
206  RAPIDJSON_UINT64_C2(0xe7109bfb, 0xa19c0c9d), RAPIDJSON_UINT64_C2(0xac2820d9, 0x623bf429),
207  RAPIDJSON_UINT64_C2(0x80444b5e, 0x7aa7cf85), RAPIDJSON_UINT64_C2(0xbf21e440, 0x03acdd2d),
208  RAPIDJSON_UINT64_C2(0x8e679c2f, 0x5e44ff8f), RAPIDJSON_UINT64_C2(0xd433179d, 0x9c8cb841),
209  RAPIDJSON_UINT64_C2(0x9e19db92, 0xb4e31ba9), RAPIDJSON_UINT64_C2(0xeb96bf6e, 0xbadf77d9),
210  RAPIDJSON_UINT64_C2(0xaf87023b, 0x9bf0ee6b)
211  };
212  static const int16_t kCachedPowers_E[] = {
213  -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980,
214  -954, -927, -901, -874, -847, -821, -794, -768, -741, -715,
215  -688, -661, -635, -608, -582, -555, -529, -502, -475, -449,
216  -422, -396, -369, -343, -316, -289, -263, -236, -210, -183,
217  -157, -130, -103, -77, -50, -24, 3, 30, 56, 83,
218  109, 136, 162, 189, 216, 242, 269, 295, 322, 348,
219  375, 402, 428, 455, 481, 508, 534, 561, 588, 614,
220  641, 667, 694, 720, 747, 774, 800, 827, 853, 880,
221  907, 933, 960, 986, 1013, 1039, 1066
222  };
223  return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
224 }
225 
226 inline DiyFp GetCachedPower(int e, int* K) {
227 
228  //int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374;
229  double dk = (-61 - e) * 0.30102999566398114 + 347; // dk must be positive, so can do ceiling in positive
230  int k = static_cast<int>(dk);
231  if (dk - k > 0.0)
232  k++;
233 
234  unsigned index = static_cast<unsigned>((k >> 3) + 1);
235  *K = -(-348 + static_cast<int>(index << 3)); // decimal exponent no need lookup table
236 
237  return GetCachedPowerByIndex(index);
238 }
239 
240 inline DiyFp GetCachedPower10(int exp, int *outExp) {
241  unsigned index = (static_cast<unsigned>(exp) + 348u) / 8u;
242  *outExp = -348 + static_cast<int>(index) * 8;
243  return GetCachedPowerByIndex(index);
244  }
245 
246 #ifdef __GNUC__
247 RAPIDJSON_DIAG_POP
248 #endif
249 
250 #ifdef __clang__
251 RAPIDJSON_DIAG_POP
252 RAPIDJSON_DIAG_OFF(padded)
253 #endif
254 
255 } // namespace internal
256 RAPIDJSON_NAMESPACE_END
257 
258 #endif // RAPIDJSON_DIYFP_H_
#define RAPIDJSON_UINT64_C2(high32, low32)
Construct a 64-bit literal by a pair of 32-bit integer.
Definition: rapidjson.h:294